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#1
Any number/0 = Undefined?

0/Any number = 0?


What is 0/0?

1? Undefined? 0?



Not maths science help thread since this isnt an assignment, just something I was wondering.
#3
Quote by XianXiuHong
Anything divided by zero is infinity.


And zero divided by anything is zero.

And any number upon itself is one?

Which is why I am confused.
#4


...

Please, stop now before you destroy the world.

Quote by luv090909
And zero divided by anything is zero.

And any number upon itself is one?

Which is why I am confused.


If any number upon itself is one, then zero is not a number.
Quote by naedauuf
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Last edited by Demonology at Sep 6, 2009,
#5
oh we discussed this a lot...technically its just not within the scope of mathematics. Its undefined. I personally think its how the universe was created... 0/0=1. Existence out of nothingness, booyakachan!
Wanted to play Bass, but then developed conscious thought...
#6
how many inifinities can fit into one infinity? im guessing an infinite amount. therefore not defined.
Jackson DXMG -> Vai Morley Wah -> Korg Black Tuner -> (Need a delay) -> Maxon OD808 -> BBE Sonic Maximizer -> ISP Noisegate -> Mesa Boogie Mark IV
#7
Quote by luv090909
And zero divided by anything is zero.

And any number upon itself is one?

Which is why I am confused.



1.Because if you try cut nothing in half, you still get nothing. If you try cut nothing into 16ths, you get nothing.


2.Because if you share 5 things among five people, you get one each, if you share 10 things among 10 people, you still get one each.
#8
Quote by Demonology


...

Please, stop now before you destroy the world.


Quote by wanksta
oh we discussed this a lot...technically its just not within the scope of mathematics. Its undefined. I personally think its how the universe was created... 0/0=1. Existence out of nothingness, booyakachan!

Nice theory
Quote by XianXiuHong
1.Because if you try cut nothing in half, you still get nothing. If you try cut nothing into 16ths, you get nothing.


2.Because if you share 5 things among five people, you get one each, if you share 10 things among 10 people, you still get one each.



So...?
Last edited by luv090909 at Sep 6, 2009,
#9
Quote by wanksta
oh we discussed this a lot...technically its just not within the scope of mathematics. Its undefined. I personally think its how the universe was created... 0/0=1. Existence out of nothingness, booyakachan!



How can mathematics create the universe? Nothing can exist outside the universe.


Quote by luv090909
So...?



I'm explaining what the numbers do.


The concept of division in mathematics is to get an equal portion of the number across the total.

Say I have four lollies and I want to share it between four people.

In a mathematical statement, it'd be 4/4 (Four divided by four)

To share the lollies equally, you give one lolly to each person and that is an equal portion.

Alternatively, you can be a selfish prick and eat them all yourself.
Last edited by XianXiuHong at Sep 6, 2009,
#10
Quote by XianXiuHong
How can mathematics create the universe? Nothing can exist outside the universe.


I'm only in high school, so ignore this particular post if need be.

Parallel universe?

The rest of my points still stand though
#11
0/0 is undetermined.

Damn college math.
P.L.U.R.

We'll choke on our vomit and that will be the end

We were fated to pretend
#12
Quote by XianXiuHong
Anything divided by zero is infinity.
No. TS is correct in saying that it is undefined.

0/0 varies depending on the context. I can't really explain it very well, but you'll learn about it if you take calculus.
kill all humans
#13
Quote by luv090909
I'm only in high school, so ignore this particular post if need be.

Parallel universe?

The rest of my points still stand though



The parallel universe theory is incorrect, if there is a parallel universe, that'd mean it exists outside ours.

That means it'd be outside of our causal horizon and nothing can ever be outside that, otherwise it simply doesn't exist.

The causal horizon is everything that has, is and ever will exist in our universe and you cannot be outside the causal horizon.
#15
Quote by XianXiuHong
How can mathematics create the universe? Nothing can exist outside the universe.


I'm explaining what the numbers do.


The concept of division in mathematics is to get an equal portion of the number across the total.

Say I have four lollies and I want to share it between four people.

In a mathematical statement, it'd be 4/4 (Four divided by four)

To share the lollies equally, you give one lolly to each person and that is an equal portion.

Alternatively, you can be a selfish prick and eat them all yourself.



I got THAT, but I dont see what that has to do with the question
#16
0 isn't a number, it's the absence of amount.
I have 1 Apple, you, have none, zero, zilch, diddly squat.
#18
Quote by grimms
0 isn't a number, it's the absence of amount.
I have 1 Apple, you, have none, zero, zilch, diddly squat.




Go back and learn basic math please.
P.L.U.R.

We'll choke on our vomit and that will be the end

We were fated to pretend
#19
Quote by XianXiuHong
You asked another question after the OP and I answered.



Oh



That wasnt supposed to be a question mark, idk why I put it there

#21
This is how I understand it.

Take 1/1 = 1

Then, 1/0.1 = 10

And:

1/0.01 = 100
1/0.000001 = 100000
1/0.0000000001 = 1000000000

...and so on. As the denominator approaches 0, the answer approaches infinity.

.: 1/0 = infinity or undefined
#22
[[THOSE WHO DON'T LEARN FROM HISTORY...]]
The first issue I came across in trying to divide by zero was that "0*1" is the same as "0*2" which is the same as "0*i" and so on. There is no conservation of what was once there; zero erases any and all past calculations, preventing us from reversing the effects of its multiplication. In other words, the reason why dividing by zero is so difficult (well, one reason why) is because multiplying by zero is so omnipotent. I decided to even the playing field.

Say hello to the system quality History, also known as "the destruction of x*0 as an omnipotent being." My most technical definition of History is as follows:
"A system with History is one which does not allow general multiplication by zero."
With History, 0*1 != 0*2 != 0*3. It is clear from the definition (and examples) that C and its subsets do not have History. It is also clear from the definition that the subset of a set without History cannot have History. (Where would the information come from, hm?)

Most of the remainder of this note involves elaborating on a set with History which I call the "Divide By Zero Vector" Number Set, or "DBZV" Set, or D. As I'll show, it includes the properties of C, as well as others...

...including the ability to divide by zero.

[[COMPLEX NUMBERS, PLAYED IN THE KEY OF D]]
Complex numbers are of the form "a + bi", where a and b exist in R. (For those who don't know, i = sqrt(-1). Any Real number multiplied by i is called an Imaginary number, and an Imaginary number added to a Real number is a Complex number.) Because a and b have no bounds, they span the whole of real numbers (consequently, bi spans all Imaginary numbers.) The "true" zero of C is when both a and b equal 0, or "0 + 0i". Thus, Complex numbers come in only two forms:
1. (a + bi)*(1/1), when a or b != 0.
2. (a + bi)*(0/1), when a and b = 0.
Since History is preserved in D, (a + bi)*(0/1) != (c + di)*(0/1) unless a = c and b = d. However, from the perspective of C, where history doesn't matter, (a + bi)*(0/1) = (c + di)*(0/1). Thus, D preserves the coefficient, or magnitude, beside "0/1".

Let's name the two forms above state 1 and state 2 respectively. They are distinguished by the core fractions 1/1 and 0/1 within them, again respectively. Straight forward, yes? In the sense of C, it's the difference between zero and not-zero.

NOTE: "(a + bi)*(0/1)" can be rewritten as "(a + bi)*(1/1)*(0/1)", "(a + bi)*(1/1)*(1/1)*(0/1)", and so-on. Since having two conflicting core fractions poses an issue, it is helpful to reinstate multiplication by zero for the special case of "0*1 = 0". Thus, "(0/1)*(1/1) = (0*1)/(1*1) = 0/1." No matter how many "1/1" you manage to pull out, it will always simplify to "0/1".

There are two notable features about numbers in D: they have a conserved magnitude and a certain state. This recognition allows us to write numbers in D in a useful way:
V = [state number, magnitude]
Where "V" stands for vector, which will be explained in more detail later, and magnitude must be a number in C such that it does not equal zero. For understanding, examine these examples of numbers from C written as numbers in D...
5 = 5*(1/1) = [1, 5]
5/2 = (5/2)*(1/1) = [1, 5/2]
0/7 = (1/7)*(0/1) = [2, 1/7]
0 = (1)*(0/1) = [2, 1]
1 = (1)*(1/1) = [1, 1]
-1 = (-1)*(1/1) = [1, -1]
5 + 7i = (5 + 7i)*(1/1) = [1, 5 + 7i]

How do addition and multiplication work in D for numbers known from C? Well, from C we know "5*2 = 10". In D, these numbers can be written as 5 = [1, 5], 2 = [1, 2], and 10 = [1, 10], or...
5*2 = 5*(1/1)*2*(1/1) = 10*(1/1) = [1, 10]
It may seem overly simple, but it's important to point out that a state 1 multiplied by a state 1 remains a state 1. This contrasts with "5*0 = 0" from C, which in D is:
5*0 = 5*(1/1)*1*(0/1) = 5*(0/1) = [2, 0]
Here, we see that a state 1 multiplied by a state 2 becomes a state 2. Not surprising again, but good to show consistency from D to C and back. The result of multiplication can be generalized for states 1 and 2 as follows:
For V = and W = [t, n],
1. If s = t, then:
V*W = W*V =
2. If s = 1, and t = 2 or vice-verse, then:
V*W = W*V = [2, m*n]

Addition is a bit more tricky, but not much. In C, we know that 3 + 4 = 7. In D, this is as follows:
3*(1/1) + 4*(1/1) = (3 + 4)*(1/1) = (7)*(1/1)
This is factoring/combining like terms, which gives us a hint at how we'd write something like 3 + 6 + 0 = 9 from C into D:
3*(1/1) + 6*(1/1) + 1*(0/1) = (3+6)*(1/1) + 1*(0/1) = 9*(1/1) + 1*(0/1)
Yessir. There IS a phantom term there. You can't see it in C, but in D--where History has recorded the addition of that 1*(0/1)--it is an important term. For example, say you want to add V and W, where V = [2, 5] and W = [2, 7]. In C, the equation would appear as 0 + 0 = 0. In D, however, V + W takes on a more informative form:
5*(0/1) + 7*(0/1) = (5+7)*(0/1) = 12*(0/1)
Huzzah? I dare to think so. Addition in D with states 1 and 2 can be generalized as follows:
For V = and W = [t, n],
1. If s = t, then:
V + W = W + V = [[A DIVISION, A NEW STATE]]
We define the inverse of A to be B such that A*B = I, where I is the identity unit of whatever system we're within. For C, I = 1. But how can we always obtain 1 for D's various states? This was the second major obstacle I came to in dividing by zero.

For state 1 numbers, the translation from C is straight-forward. For example, we know from C (assumed to be a subset of D since we expect all properties in C to work in D; it wouldn't be cool to divide by zero if we abandoned Complex numbers.) that "4*(1/4) = 1". In D, this reads as:
4*(1/1)*(1/4)*(1/1) = (4*1/4)*(1/1) = (1)*(1/1) = [1, 1]
The same result is obtained from any multiplication of known C inverses. The generalized result is as follows:
For V = and W = [t, n] where V and W are state 1, V and W are inverses if and only if V*W = [1, 1]
Alternatively:
The inverse of V = if s = 1 is W, such that W =

For state 2 numbers, we come across an issue of not knowing what to consider the inverse. We can't base this on C because C doesn't know how to handle it either. Instead, we rely on a "Multiplicative Identity" field axiom (if my hopes work out, I will eventually prove D to be a field) which states:
"1*x = x", or "1 = x/x"
Like I said earlier, because of zero's omnipotence in C, information on what multiplies by zero isn't preserved. Thus, each zero is indistinguishable from all others. In D, we can tell the difference between zeros. In fact, earlier we made sure that that only way to obtain zero through multiplication is via "1*0 = 0". Look familiar? This unique multiplication situation allows zero to apply to the Multiplicative Identity field axiom.
In more epic phrasing: "1/1 = 0/0 = (0*1)/(1*0) = (0/1)*(1/0)"
Damn straight. We thus have a relation which bridges state 1 numbers, state 2 numbers, AND division by zero. Awesome, right? I think so.

Before we can handle the inverse of a state 2 number though, we have to define the new state represented in the epically phrased relation. Although we've seen the core fractions "0/1" and "1/1" before, we've never come across "1/0". Let's define this as a new state... a state 0, if you will. State 0 is distinguished by the core fraction "1/0". Examples of such are as follows:
7/0 = (7)*(1/0) = [0, 7]
(1/2)/0 = (1/2)*(1/0) = [0, 1/2]
5/0 + 6/0 = (5)*(1/0) + (6)*(1/0) = (5+6)*(1/0) = (11)*(1/0) = [0, 11]

Now, if W is the inverse of V where V = [2, n], then
W*V = [1, 1]
W*[2, n] = [1, 1]
W*(n)*(0/1) = (1)*(1/1)
W*(0/1)*(1/0) = (1/n)*(1/1)*(1/0)
W*(1/1) = (1/n)*(1/0)
W = (1/n)*(1/0) = [0, 1/n]
Thus, the inverse of a state 2 is a state 0, with the magnitude flipped. (It was expected, but it's still nice to see the calculations work out.) If you begin the previous derivation with a state 0 instead of a state 2, you obtain the opposite result. In general:
The inverse of V = [0, n] is W, such that W = [2, 1/n]
The inverse of W = [2, 1/n] is V, such that V = [0, n][[THE GOAL ACHIEVED]]
Say you have 7/(2*0), which was what I was given to "solve" when this whole thing began (either that or something similar.)
First, write it in D-acceptable form:
7/(2*0) = (7/2)*(1/0) = [0, 7/2]
Take the inverse and you get:
[0, 7/2] --> [2, 2/7] = (2/7)*(0/1)
In C, where History is ignored, this can be written as "0". In D, however, we can take the inverse again...
[2, 2/7] --> [0, 7/2][[TO BE CONTINUED]]
There are still some holes to work out (for instance: try squaring a state 0 or state 2), but I'm going to keep working at this until I can prove--or disprove--D as a field. My next note will include a discussion of numbers in D as being vectors, an extended state system, and may explore attempts to graph in D. If I figure out exponents in D, I'll be sure to include that as well.


Edit:This is a friend of mine, who is quite the smart man, he decided to try and divide by zero, and succeeded by using vectors and axioms to actually divide by zero. If anyone is interested i will post the second part.
The Set Up
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4-1986 Charvel Model 5
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Last edited by The__Chill at Sep 6, 2009,
#23
Please say you copypasted that ^
- - - - - - - -
When I think of the perpetual journey through life
When it always feels like autumn
The wind moves slowly to the north
And the flowers die
Rain falls in my dreams

- - - - - - - -
#24
Quote by XianXiuHong
How can mathematics create the universe? Nothing can exist outside the universe.
I suppose he meant the creation of matter from nothing. I don't know nuffin, but I always just think that the universe was not created, it just existed from the beginning.
I have a ponytail fetish.
..And a labcoat fetish. SCIENCE!
Last edited by AntiG3 at Sep 6, 2009,
#26
0/0 is undefined, but tends towards a limit of 1.
0.1/0.1 = 1
0.01/0.01 = 1 etc.

Quote by NakedInTheRain
This is how I understand it.

Take 1/1 = 1

Then, 1/0.1 = 10

And:

1/0.01 = 100
1/0.000001 = 100000
1/0.0000000001 = 1000000000

...and so on. As the denominator approaches 0, the answer approaches infinity.

.: 1/0 = infinity or undefined


And yes, I agree.
Last edited by National_Anthem at Sep 6, 2009,
#27
Quote by AntiG3
I suppose he meant the creation of matter from nothing. I don't know nuffin, but I always just think that the universe was not created, it just existed from the beginning.



To say beginning implies that there was a moment of creation.

If the universe were to be infinite, the night sky would be totally bright because the light from distant stars will have had an infinite amount of time to reach us.


The universe is and will continue to expand but that's just ongoing, to say it's infinite means that it has always existed and has no beginning or end.
#28
The closer you get to zero the larger the number is, so then anything divided by zero is infinity.
#31
Any number divided by 0 is undefined, including 0.

/thread.


Originally Posted by evening_crow
Quoting yourself is cool.


WARNING: I kill threads.
#32
Quote by XianXiuHong
Wat.


Sorry, the closer the number you divide by zero is to zero, the larger the number will be.

That will mean that anyting : zero = infinity.
#34
Quote by evening_crow
Any number divided by 0 is undefined, including 0.

/thread.




This thread is made because TS want to know what's behind the "undefined".
#36
Quote by GisleAune
This thread is made because TS want to know what's behind the "undefined".

Let's just say it's a mathematical glitch so that everyone can comprehend it.
Originally Posted by evening_crow
Quoting yourself is cool.


WARNING: I kill threads.
#37
ok, Firstly thanks to AntiG3 for recognizing the vague metaphoric quality in my statement, i merely did not want to overload this thread. Secondly, the causal horizon is a scientific theory disputed beyond belief...if you want to go in that direction quote the event horizon. However beyond this matter CAN exist (Black holes). Also if what you refer to as "causal horizon" should exist in this manner, matter could exist outside of it (Weakly interacting massive particles) that are simply impossible (by definition) to detect.

glad that the false mention of olbers paradox has been cleared up.

Going back to the original question on subtraction. If one would look into the axiomix definition of division on the Real numbers, one would see that Zero is precluded from this definition. Hence, since mathematics is axiomix, it is simply not possible to divide zero by zero. There can be no meaningful answer deduced from this process.

as for any real number divided by zero, anyone who has ever taken a glimpse at limits will realize that they all tend towards inifinity. This has been researched and explained and is used frequently in cardinal maths.
Wanted to play Bass, but then developed conscious thought...
#38
Quote by National_Anthem



I read some of it and then scanned over the rest.

Is it basically that the universe is infinite but star's lifespans aren't and that's why the night sky isn't totally bright? And that the spacing of stars isn't equal?

With an infinite amount of space, there would be basically stars scattered everywhere all different distances but with enough space to fill the entire night sky and all having had an infinite amount of time to reach us.

I'm starting to not make sense now, I'm still trying to wrap my head around all of this universe stuff.
#39
Quote by wanksta
ok, Firstly thanks to AntiG3 for recognizing the vague metaphoric quality in my statement, i merely did not want to overload this thread. Secondly, the causal horizon is a scientific theory disputed beyond belief...if you want to go in that direction quote the event horizon. However beyond this matter CAN exist (Black holes). Also if what you refer to as "causal horizon" should exist in this manner, matter could exist outside of it (Weakly interacting massive particles) that are simply impossible (by definition) to detect.

glad that the false mention of olbers paradox has been cleared up.

Going back to the original question on subtraction. If one would look into the axiomix definition of division on the Real numbers, one would see that Zero is precluded from this definition. Hence, since mathematics is axiomix, it is simply not possible to divide zero by zero. There can be no meaningful answer deduced from this process.

as for any real number divided by zero, anyone who has ever taken a glimpse at limits will realize that they all tend towards inifinity. This has been researched and explained and is used frequently in cardinal maths.


Sorry if i'm wrong, but are you implying that 0 is not a real number?

It is.
Originally Posted by evening_crow
Quoting yourself is cool.


WARNING: I kill threads.
#40
Quote by evening_crow
Sorry if i'm wrong, but are you implying that 0 is not a real number?

It is.


No, he was saying that division by zero is precluded from the definition of division of real numbers, not the definition of real numbers.
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